TY - JOUR
T1 - Neuron model with conductance-resistance symmetry
AU - Deng, Bo
N1 - Funding Information:
The author acknowledges a generous summer visitors fellowship of 2017 from the Mathematics and Science College, Shanghai Normal University, Shanghai, China.
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/11/28
Y1 - 2019/11/28
N2 - This paper is to derive a mathematical model for neuron by imposing only a principle of symmetry that two modelers must obtain the same model when one models the conductances of ion channels and the other models the channels' resistances. Conductance-voltage characteristics for ion transport channels and protein gating channels are both derived. They are expressed as products of maximal conductances and opening probabilities for both types of channel. It gives an explanation to the role of spontaneous firing of individual channel pores and to the origin of leak current. The model has a better fit to a classical data than the Hodgkin-Huxley model does. It can also be reduced to a 2-dimensional model qualitatively similar to the FitzHugh-Nagumo equation and be expanded to a model of three ion channels capable of spike bursts.
AB - This paper is to derive a mathematical model for neuron by imposing only a principle of symmetry that two modelers must obtain the same model when one models the conductances of ion channels and the other models the channels' resistances. Conductance-voltage characteristics for ion transport channels and protein gating channels are both derived. They are expressed as products of maximal conductances and opening probabilities for both types of channel. It gives an explanation to the role of spontaneous firing of individual channel pores and to the origin of leak current. The model has a better fit to a classical data than the Hodgkin-Huxley model does. It can also be reduced to a 2-dimensional model qualitatively similar to the FitzHugh-Nagumo equation and be expanded to a model of three ion channels capable of spike bursts.
KW - Conductance-resistance symmetry
KW - FitzHugh-Nagumo equations
KW - Hodgkin-Huxley equations
KW - Opening probability for ion transport channel
KW - Opening probability for protein gating channel
KW - Spontaneous firing
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U2 - 10.1016/j.physleta.2019.125976
DO - 10.1016/j.physleta.2019.125976
M3 - Article
AN - SCOPUS:85072175446
SN - 0375-9601
VL - 383
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 33
M1 - 125976
ER -